Question

find the limit
lim x approaches 13 for (13-x)/(x^2-169)

Answer 1

\[\lim_{x \rightarrow 13} \frac{(13-x)}{(x^2-169)} \]
\[=\lim_{x \rightarrow 13} \frac{(13-x)}{(x^2-13^2)} \]
\[=\lim_{x \rightarrow 13} \frac{(13-x)}{(x+13)(x-13)} \]
\[=\lim_{x \rightarrow 13} \frac{(13-x)}{-(x+13)(13-x)} =\lim_{x \rightarrow 13} \frac{-1}{(x+13)} \]
Applying limit we find
\[ = \frac{-1}{(13+13)} = \frac{-1}{26} \]

Answer 2

@nlpowell

Answer 3

Thank you.